The NP-completeness of some edge-partitioning problems
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Some NP-complete edge packing and partitioning problems in planar graphs
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not share edges. Bernáth and Király proved that this decision problem is NP-complete and asked if the same result holds when restricting to planar graphs. Simila...
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